Question

a board leaning against a wall forms a 65° angle as shown in the figure below. what angle does the board make with the floor? note: the figure is not drawn to scale. options: 25°, 35°, 65°, 90°

Explanation:

Step1: Recall the property of triangle angles

The sum of angles in a right - triangle is \(180^{\circ}\). One angle is \(90^{\circ}\) (right angle between wall and floor), and another is \(65^{\circ}\). Let the angle with the floor be \(x\).

Step2: Apply the angle - sum formula

Using the formula \(x + 65^{\circ}+90^{\circ}=180^{\circ}\). Then \(x=180^{\circ}-(90^{\circ} + 65^{\circ})\).

$$x=180^{\circ}-155^{\circ}=25^{\circ}$$

Answer:

A. \(25^{\circ}\)